{
  "annotation_id": "4e5945fe-cdf3-4590-98d1-602dfcce0a2e",
  "date_created": "2026-03-02T18:02:27.507000Z",
  "date_modified": "2026-03-02T18:02:27.507000Z",
  "file_hash": "4d1212ddf72014c544adf737ec1d090832210a48adef7946e21eb165550fabb5",
  "private": false,
  "record": {
    "abstract": "The majorization theory has been applied to analyze the mathematical\nstructure of quantum algorithms. An empirical conclusion by numerical\nsimulations obtained in the previous literature indicates that step-by-step\nmajorization seems to appear universally in quantum adiabatic algorithms. In\nthis paper, a rigorous analysis of the majorization arrow in a special class of\nquantum adiabatic algorithms is carried out. In particular, we prove that for\nany adiabatic algorithm of this class, step-by-step majorization of the ground\nstate holds exactly. For the actual state, we show that step-by-step\nmajorization holds approximately, and furthermore that the longer the running\ntime of the algorithm, the better the approximation.",
    "arxiv_id": "quant-ph/0606015",
    "authors": [
      "Zhaohui Wei",
      "Zhengfeng Ji",
      "Mingsheng Ying"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.042320",
    "journal_ref": "Phys. Rev. A 74, 042320(2006)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Majorization in Quantum Adiabatic Algorithms",
    "url": "https://arxiv.org/abs/quant-ph/0606015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "37cbc614-ea91-481c-8eb0-422ac9f10453",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}